James Clerk Maxwell was a physicist of the caliber of Einstein and Newton and arguably comparable to them in the scope of his thought. Although probably best known to mathematicians for the equations that bear his name, Maxwell was a broadly gifted thinker and synthesizer who made significant contributions in statistical mechanics, optics and control theory as well as in electromagnetics. He developed the concept of a field (as, for example, the electric or magnetic field) that continues to be a powerful conceptual tool in physics. It is not so well known that Maxwell was a skilled writer who produced works of elegance and clarity on a variety of scientific subjects.
Figures of Thought: A Literary Appreciation of Maxwell’s Treatise on Electricity and Magnetism is an unusual discussion of a scientific figure’s work that focuses as much on literary devices and style as it does on physics. However, this is no piece of fluff. The author, Thomas Simpson, has spent a long career studying Maxwell, and he is ardent about reconciling the cultures of science and the arts. Early in the book he writes:
A scientific work evidences literary character when it is imbued with a vision or a goal towards which its parts are organized throughout. Achieving this organization is the business of the art of poetics, which teaches us that there must be a story line with a beginning, middle and end. The four parts of the Treatise do unfold this way… The mathematical statements that the world knows as ‘Maxwell’s equations’ encapsulate not only a coherent view of electricity and magnetism as a whole, but a new way of look at physical processes more generally. All this, shaped from the beginning to tell the story of the field, is a truly poetic conception.
The book first addresses the rhetorical structure of Maxwell’s Treatise, particularly Part IV of that work (where Maxwell combines electricity and magnetism and essentially invents electrodynamics). Simpson catalogues the “tropes” that define the work, where trope means a turn of expression that serves to shift the mind’s attention from one aspect of a subject to another, thereby making it possible to see the subject in a new light. He sees a variety of tropes in Maxwell: analytical, geometrical, diagrammatic, analogical, experimental and formal. So, for example, an identity — derived via Green’s Theorem — is called an analytical trope, whereas the comparison of the electrostatic field to an elastic body under strain is an analogical trope.
The second part concentrates on what might be called the “plot” of Maxwell’s work, what Simpson calls the poetic argument. In the culmination of the Treatise, Maxwell pulls together the work of Faraday, Ampère, Oersted and Lagrange to assemble the pieces that ultimately lead to his famous equations. Simpson’s concluding section summarizes his idea that the Treatise is dedicated to the expression of one central idea — the notion of a field — and that the whole work (and nothing less) is necessary to capture that idea.
This is an intriguing book that constantly challenges boundaries between the scientific and the literary. It also offers weird juxtapositions: surface integrals and tropes, Ampère’s law and stylistic contrast, rhetorical power and Lagrange’s equations. Here, not completely successfully, the two cultures meet.
Bill Satzer (firstname.lastname@example.org) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.